Final answer:
The lowest possible payoff in a decision tree related to the Prisoner's Dilemma typically occurs when neither party cooperates, resulting in a suboptimal outcome for all involved. Without the complete decision tree, the exact lowest payoff cannot be determined.
Step-by-step explanation:
The question posed appears to be related to decision-making in the context of game theory, specifically the Prisoner's Dilemma. The dilemma illustrates how rational individuals might not cooperate, even if it seems that it is in their best interest to do so. When companies or individuals face a decision tree with various payoffs depending on the actions of the other party, they must consider the lowest possible payoff as a scenario where neither party cooperates. This often leads to a suboptimal payoff for both parties. However, without the complete decision tree, we cannot definitively state what the lowest payoff would be.
In the Prisoner's Dilemma, which is a common example in game theory, two prisoners (or firms, in a business context) face a decision on whether to cooperate with each other or not. The best collective outcome occurs if both cooperate, but the fear of the other party defecting can lead both to choose non-cooperation, resulting in a lower payoff for both. If we apply this to Becky and Sarah or firms A and B, mentioned in the provided information, it's likely that the worst outcome is when both parties choose not to cooperate, potentially increasing output but earning lower profits, such as $400 each, instead of achieving a higher combined profit by acting like a monopolist.